

    \filetitle{sspace}{State-space matrices describing the model solution}{model/sspace}

	\paragraph{Syntax}

\begin{verbatim}
[T,R,K,Z,H,D,U,Omg] = sspace(M,...)
\end{verbatim}

\paragraph{Input arguments}

\begin{itemize}
\tightlist
\item
  \texttt{M} {[} model {]} - Solved model object.
\end{itemize}

\paragraph{Output arguments}

\begin{itemize}
\item
  \texttt{T} {[} numeric {]} - Transition matrix.
\item
  \texttt{R} {[} numeric {]} - Matrix at the shock vector in transition
  equations.
\item
  \texttt{K} {[} numeric {]} - Constant vector in transition equations.
\item
  \texttt{Z} {[} numeric {]} - Matrix mapping transition variables to
  measurement variables.
\item
  \texttt{H} {[} numeric {]} - Matrix at the shock vector in measurement
  equations.
\item
  \texttt{D} {[} numeric {]} - Constant vector in measurement equations.
\item
  \texttt{U} {[} numeric {]} - Transformation matrix for predetermined
  variables.
\item
  \texttt{Omg} {[} numeric {]} - Covariance matrix of shocks.
\end{itemize}

\paragraph{Options}

\begin{itemize}
\tightlist
\item
  \texttt{\textquotesingle{}triangular=\textquotesingle{}} {[}
  \emph{\texttt{true}} \textbar{} \texttt{false} {]} - If true, the
  state-space form returned has the transition matrix \texttt{T} quasi
  triangular and the vector of predetermined variables transformed
  accordingly; this is the default form used in IRIS calculations. If
  false, the state-space system is based on the original vector of
  transition variables.
\end{itemize}

\paragraph{Description}

The state-space representation has the following form:

\begin{verbatim}
[xf;alpha] = T*alpha(-1) + K + R*e

y = Z*alpha + D + H*e

xb = U*alpha

Cov[e] = Omg
\end{verbatim}

where \texttt{xb} is an nb-by-1 vector of predetermined
(backward-looking) transition variables and their auxiliary lags,
\texttt{xf} is an nf-by-1 vector of non-predetermined (forward-looking)
variables and their auxiliary leads, \texttt{alpha} is a transformation
of \texttt{xb}, \texttt{e} is an ne-by-1 vector of shocks, and
\texttt{y} is an ny-by-1 vector of measurement variables. Furthermore,
we denote the total number of transition variables, and their auxiliary
lags and leads, nx = nb + nf.

The transition matrix, \texttt{T}, is, in general, rectangular nx-by-nb.
Furthremore, the transformed state vector alpha is chosen so that the
lower nb-by-nb part of \texttt{T} is quasi upper triangular.

You can use the
\texttt{get(m,\textquotesingle{}xVector\textquotesingle{})} function to
learn about the order of appearance of transition variables and their
auxiliary lags and leads in the vectors \texttt{xb} and \texttt{xf}. The
first nf names are the vector \texttt{xf}, the remaining nb names are
the vector \texttt{xb}.


